Localized arc filament plasma actuators for noise mitigation and mixing enhancement

ABSTRACT

A device for controlling fluid flow. The device includes an arc generator coupled to electrodes. The electrodes are placed adjacent a fluid flowpath such that upon being energized by the arc generator, an arc filament plasma adjacent the electrodes is formed. In turn, this plasma forms a localized high temperature, high pressure perturbation in the adjacent fluid flowpath. The perturbations can be arranged to produce vortices, such as streamwise vortices, in the flowing fluid to control mixing and noise in such flows. The electrodes can further be arranged within a conduit configured to contain the flowing fluid such that when energized in a particular frequency and sequence, can excite flow instabilities in the flowing fluid. The placement of the electrodes is such that they are unobtrusive relative to the fluid flowpath being controlled.

This application claims the benefit of the filing date of U.S.Provisional Application No. 60/499,505, filed Sep. 2, 2003.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under NAS3-02116 awardedby NASA. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

The present invention relates to the control of high-velocity fluidstreams, such as those present in core and fan streams exhausting a gasturbine engine, and more particularly to the manipulation of such fluidstreams through localized arc filament plasmas to affect noise radiationfrom and mixing rate in the mixing layers of these streams.

Noise radiation from an aircraft gas turbine engine is the dominantcomponent of noise during takeoff and a major component during landing.As such, it is becoming an important issue for both commercial andmilitary aircraft that are operating at considerably closer proximity topopulation centers, as there is mounting pressure to reduce noisepropagated to adjacent communities. Commercial subsonic aircraft enginemanufacturers have been able to satisfy increasingly stringentenvironmental noise regulations by using larger by-pass ratio engines.Unfortunately, the sheer physical size of current commercial subsonicaircraft engines is such that even larger bypass ratio engines are notpractical. Additionally, in future supersonic commercial aircraft andalso in high-performance military aircraft, large bypass ratio enginesare not a viable option because of the performance penalties that such adesign would incur.

It has been known for quite some time that large-scale coherentstructures in jets are responsible for the entrainment and mixing ofexhaust systems, and that their dynamical I processes are responsiblefor a major portion of far field noise radiation. Research has indicatedthat these large-scale spanwise coherent structures in two-dimensionalor ring-like coherent structures in axisymmetric jets or mixing layers,become more three-dimensional and less coherent as the compressibilitylevel (which is generally proportional the ratio of velocity differenceacross the mixing layer to the average speed of sound in the twostreams) is increased. This phenomenon renders these structures lessamenable to control strategies similar to those traditionally used inincompressible and low Reynolds number flows. In contrast to theselarge-scale structures, longitudinal (streamwise) large-scale vorticesdo not seem to be much affected by compressibility. Thus, the use ofstreamwise vortices appears to be a logical approach in controllingmixing and consequently controlling the far field acoustic radiation inhighly compressible jets.

In the past, several techniques have been explored in generatingstreamwise vortices. For example, small tabs or chevrons attached to thenozzle exit and used as streamwise vortex generators were found to be aneffective device in enhancing mixing and altering noise characteristicsin both incompressible and compressible jets, due to the presence of aspanwise pressure gradient set up in front of a tab, which since itprotrudes into the flow, generates a spanwise pressure gradientregardless of whether the flow is subsonic or supersonic. In addition tostreamwise vortices generated due to the spanwise pressure gradient, thestreamwise pressure gradient generated by a tab promotes the developmentof robust spanwise vortices. Although the use of tabs and relatedprotrusions to enhance mixing is effective in both incompressible andcompressible flows, such use results in thrust losses due to theblockage effects. Gentler tabs, such as chevrons, can be used to reducethis thrust loss; however, their smaller profile necessitates weakerstreamwise vortices and thus less mixing enhancement or noisealteration. Moreover, it is also beneficial to minimize the performancepenalties associated with flowstream protrusions by having them deployonly during certain operational conditions (for example, during takeoffand landing in aircraft applications). Such an on-demand system requirescomplex tabs/chevrons geometries, ancillary actuation hardware andcontrollers, thereby exacerbating system complexity, weight and cost.

An alternative technique for generating streamwise vortices is the useof simple nozzle trailing edge modifications or cutouts. These cutoutsare similar to chevrons, except that they do not protrude into the flow.Prior research has shown that such modifications have been effective inproducing streamwise vortices that in turn generate enhanced mixing inincompressible axisymmetric jets, although the effectiveness of trailingedge modifications heavily depend on the flow regime. It was found thatthe use of trailing edge modifications enhanced mixing significantly inthe underexpanded cases and moderately in the overexpanded cases. It wasalso found that the trailing edge modified nozzles substantially reducedthe broadband shock associated noise radiation for both theunderexpanded and overexpanded flow regimes, but did not significantlyalter the noise field for the ideally expanded flow condition. While itis believed that the mechanism employed by nozzle trailing edgemodifications to produce streamwise vortices is still a spanwisepressure gradient, it appears that such effects are relatively small insubsonic jets and heavily flow regime-dependent in supersonic jets.There is also evidence that trailing edge modifications exhibit a strongeffect on the rate of jet mixing and thus noise radiation.

Another technique involves the use of fluidics, where pressurized fluid(typically air) is introduced into the flowpath to force an instabilitytherein. Fluidic injection has not been entirely successful for use inhigh-speed flows for two main reasons. First, instability frequencies inhigh-speed flows are quite high, which necessitates that any actuationmechanism must possess high bandwidth capability. Second, fluid flowswith high Reynolds numbers (such as those found in high subsonic andsupersonic flow velocities) possess large dynamic loading within a noisyenvironment, which require high amplitude forcing. The lack of theavailability of actuators with high bandwidth and high amplitude hasbeen one of the main obstacles in fluidic control of high-speed flows.Efforts have been made to force shear layers in high Reynolds number atthe jet column frequency; however, the required forcing amplitude ismuch higher than that used traditionally. Similarly, efforts have beenmade to develop high bandwidth and amplitude fluidic actuators. The maindrawback of such fluidic actuators is the difficulty of establishing areference time (or phase), for without such a reference time, theactuators cannot be used to force various azimuthal modes inaxisymmetric jets. Since it is believed that certain of these azimuthalmodes are instrumental in achieving noise reduction, the presence of anactuator that can excite such instabilities is highly desirable.

Still another technique that has been used in recent years exploitselectric discharge plasmas for flow control. In a typical plasma-basedapproach, intense, localized and rapid heating is produced in thehigh-current pulsed electric discharges and pulsed optical discharges.This rapid near-adiabatic heating results in an abrupt pressure jump inthe vicinity of the current-carrying filament. These pressure jumps inturn produce shock waves in supersonic flows, which can considerablymodify the supersonic flow over blunt bodies and in supersonic inlets.Therefore, the rapidly heated regions act similar to physical geometryalterations (such as the tabs and trailing edge cutouts discussedearlier) in the flow but do so for short time durations. Various methodsof plasma generation, including direct current (DC), alternating current(AC), radio frequency (RF), microwave, arc, corona, and spark electricdischarges, as well as laser-induced breakdown, have been used toinitiate plasma-based fields for flow control.

Previous investigations into plasma-based flow control have mainlyfocused on viscous drag reduction and control of boundary layerseparation in low-speed flows, as well as shock wave modification andwave drag reduction in supersonic and hypersonic flows. In the previoushigh-speed research, spatially distributed heating induced by AC or RFglow discharges has been used to produce weak disturbances in thesupersonic shear layer or to weaken the oblique shock in the supersonicinviscid core flow. These experiments have been conducted at fairly lowstatic pressures, for example, at stagnation pressures of between 0.3and 1.0 atmosphere with Mach numbers between two and four. This allowedinitiating and sustaining diffuse glow discharges, which weakly affectedrelatively large areas of the flow. The main mechanism of the plasmaflow control in these previous studies is heating of the flow by theplasma. In low-speed flows, the dominant plasma flow control mechanismis flow entrainment due to momentum transfer from high-speed directedmotion of ions (i.e. electrical current) to neutral species (i.e. bulkflow) in the presence of a strong electric field. At these conditions,the ion velocity can be very high (for example, approximately 1000meters per second for typical electric fields of 10 kilovolts percentimeter at one atmosphere). Although this approach was demonstratedto significantly vary the skin friction coefficient and to control theboundary layer separation in low-speed flows (at flow velocities up to afew meters per second), its applicability to high-speed flows isunlikely. The main disadvantage of this technique is that the ion numberdensity in non-equilibrium plasmas is very low (for example, typicalionization fractions n_(i)/N are between approximately 10⁻⁸ and 10⁻⁶),which limits the momentum transfer to the neutral species flow; suchlimited momentum transfer is not conducive for high flow velocities.Another disadvantage of this approach is the high power consumption ofnon-equilibrium plasmas (typically between approximately 10 to 100 wattsper cubic centimeter), due to the fact that only a very small fractionof the total input power (often well below 1%) goes to direct momentumtransfer from the charged species to the neutral species. The rest ofthe power (more than 90%) is spent on excitation of vibrational andelectronic levels of molecules by electron impact, followed by flowheating during relaxation processes. This makes affecting large areas ofthe flow by such plasmas prohibitively expensive.

What is needed are actuators that can exploit streamwise vorticitygeneration, manipulation of jet instabilities, or a combination of thetwo techniques to facilitate noise reduction and flow mixing in highspeed fluid flow environments. What is also needed are such actuatorsthat can provide high amplitude, high bandwidth forcing whilesimultaneously being capable of withstanding harsh environments, such asthose found in air-breathing turbomachinery and related power-generatingequipment. What is additionally needed are actuators that do notinterfere with fluid flow in the jet by protruding into the jet stream.

SUMMARY OF THE INVENTION

These needs are met by the present invention, where one or morelocalized arc filament plasma actuators (in the form of pairedelectrodes) include both high amplitude and high bandwidth withoutrequiring the use of high-power pulsed lasers, focused microwave beams,or electrodes protruding into the flow. The present inventors havediscovered that the use of repetitively pulsed high-energy dischargesemanating from electrodes spatially distributed on a conduit surface canproduce streamwise vortices of desired distribution and kind. Aspreviously mentioned, flow perturbations can produce spanwise vorticeswhere, due to the nature of jet flow, they are generated naturally byjet instabilities. Thus, while the inventors' intent focuses on thegeneration and use of streamwise vorticity, it will be appreciated bythose skilled in the art that the production of spanwise vorticity couldalso have utility, and that the present invention could be adapted toenhance or weaken such spanwise vorticity, depending upon theapplication. The present invention can be configured to distributeelectrodes and energize them with proper excitation frequencies in sucha way as to influence shear layer instabilities.

The present inventors have discovered that the use of repetitivelypulsed high-energy discharges can produce strong localized pressureperturbations in subsonic and supersonic flows, at static pressures of1.0 atmosphere, with no fundamental limitations at higher or lowerpressures. These localized pressure perturbations are hefty enough toeffectively act like a physical obstacle (such as a flap, tab or thelike) suddenly placed in the flowpath. In the present context, the term“localized” and its variants represent changes made in the area of theduct, conduit or related flowpath that is immediately adjacent theelectrodes or related plasma-producing terminals. The proximity of theplasma to the solid surface (i.e., the nozzle wall) greatly improvesplasma stability, reducing the chance of plasma being blown off by theincident high-speed gas (such as air or exhaust gas) flow. Repetitivepulsing of the discharge would enable control over these pressureperturbation obstacles by having an arc filament initiated in the flowgenerate rapid (on the time scale of down to a few microseconds)localized heating up to high temperatures, which produces a concomitantlocalized pressure rise in the flow near the electrodes. Consequently,when the arc filament is on, the electrode functions as theaforementioned physical obstacle, similar to a small tab inserted intothe flow. Advantages associated with the present invention include: theability of the electrodes to modify the flow field on-demand, therebyallowing the electrodes to be turned on and off to minimize powerconsumption and potential losses when actuation is not necessary;avoidance of changing the geometry of the flowpath; avoidance of usingmoving parts that can wear out; and the controlling of mixing and noisein the jet by either excitation of flow instabilities, generatingstreamwise vorticity of desired frequency and strength, or by acombination of the two techniques.

Regarding the excitation of flow instabilities (such as theaforementioned shear layer instabilities), the present inventors havedetermined that the electrodes of the present invention can exciteaxisymmetric and azimuthal instabilities in high-speed jets for noisemitigation and mixing control, as well as demonstrating that streamwisevortices can be generated in non-axisymmetric (for example, rectangular)exhaust nozzles in subsonic or supersonic flow conditions. While thepresent inventors have tested the technique in limited geometries andflow conditions, there is no physical limitation imposed on thetechnique in terms of Mach number or the nozzle geometry.

According to a first aspect of the invention, a fluid stream flowmodification system is disclosed. The system includes a fluid streamconduit configured to receive flowing fluid from a fluid source, and anarc generator cooperative with the conduit such that upon systemoperation, an arc filament plasma is formed that produces a localizedperturbation in a portion of the fluid stream. The arc generatorincludes numerous electrodes disposed adjacent the fluid stream. Thearrangement of the electrodes is such that they do not substantiallyprotrude into the fluid stream, thereby by avoiding unnecessary flowdisturbances. This unobtrusive profile, coupled with the on-demandnature of the flow perturbations, results in overall improvements in theflow of fluid in the stream. The electrodes produce localized (ratherthan global) perturbation that generates streamwise vorticity in thelocalized portion of the fluid stream. As previously mentioned, spanwisevortices are generated naturally by jet instabilities, and the presentinvention can be configured to enhance or weaken these spanwise vorticesas needed. In addition to the electrodes, the system includes an energysource that can impart enough energy to the electrodes such that an arcfilament plasma capable of generating the localized perturbation isformed.

In one optional embodiment, the energy source is an electric currentsource capable of high voltage operation. In one form, the electrodesare placed substantially flush with the surface of the conduit adjacentthe fluid stream. Thus, for example, where the conduit is a duct, theelectrodes form a substantially flush fit with the inner duct wall. Theelectrodes can be configured as an array of one or more rows, whereconfigurations employing a plurality of rows can be arranged such thateach successive row is axially downstream in the conduit relative to itsimmediately preceding row. In another form, the electrodes can bedisposed adjacent a trailing edge of the conduit, as well as about theconduit's periphery. In configurations where the conduit is a duct, bothsubstantially axisymmetric and non-axisymmetric constructions arepossible, where in the latter, the duct could be, among other shapes,rectangular. In the present context, the term “substantially” isutilized to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. As such, it refers to an arrangement of elements orfeatures that, while in theory would be expected to exhibit exactcorrespondence or behavior, may in practice embody something slightlyless than exact. The term also represents the degree by which aquantitative representation may vary from a stated reference withoutresulting in a change in the basic function of the subject matter atissue.

In another option, a controller can be coupled to the generator suchthat the generation of the localized perturbations at the electrodesoccurs at predetermined times. For example, the electrodes can beenergized either simultaneously or at staggered time intervals. Suchstaggering can promote the excitation of a desired instability orrelated perturbation pattern. The resistance of the conduit to theexcess heat generated by the arc filaments can be made enhanced byvarious approaches. In one, the conduit can be made from a refractorymaterial, such as a ceramic or ceramic composite. In another, a coolantsupply can be placed in heat exchange relationship with the conduit toavoid excessive temperatures.

A significant difference of the localized arc filament plasma electrodesof the present invention over plasma electrodes developed previously(such as surface glow discharge-based devices) is that the presentelectrodes are designed to generate localized, high-temperature arcfilaments rather than large surface area, low-temperature,non-equilibrium plasmas. Applying high voltage of select frequency tothe electrode would generate a periodic arc and corresponding Joule heatrelease, resulting in high-frequency excitation of the flow. Inaddition, using two or more properly phased electrodes at the same timewould allow excitation of specific flow instabilities (for example,azimuthal modes) by varying both the excitation frequency and the phaseshift between individual electrodes. This effect, together with thesmall size of the filaments would make it possible to producesignificant changes in the flow without a concomitant level of powerconsumption. Thus, two of the electrodes can be configured to cooperatewith each other to define an actuator that produces the arc filamentthat in turn produces the localized perturbation. In a similar way, two(or more) electrodes could each be coupled to a ground electrode todefine the actuator.

According to another aspect of the invention, an exhaust system isdisclosed. The system includes an exhaust duct defining an exhauststream flowpath surface, and an arc generator cooperative with theexhaust duct. Activation of the arc generator during the flow of theexhaust stream causes an arc filament plasma to be formed, which in turnproduces a localized perturbation in a portion of the exhaust streamthat is adjacent the arc filament formed around the electrodes. The arcgenerator is made up of a plurality of electrodes disposed adjacent theportion of the exhaust stream. As before, the electrodes do notsubstantially protrude into a flowpath defined by the exhaust stream.The electrodes are arranged such that when energized, the localizedperturbation generates streamwise vorticity in the portion of theexhaust stream nearest the electrodes. In addition to the electrodes,the arc generator includes an energy source coupled to the electrodesand configured to impart enough energy to them such that an arc filamentplasma capable of generating the localized perturbation is formed.

Optionally, the electrodes are disposed in the exhaust duct to define asubstantially flush fit with the inner (exhaust stream flowpath)surface. As with the previous aspect, the exhaust duct can besubstantially axisymmetric or substantially non-axisymmetric. Also asbefore, the electrodes are arranged around a substantial periphery ofthe exhaust stream flowpath surface. A controller can be coupled to thearc generator to energize the electrodes according to a predeterminedsequence; such an arrangement is beneficial in exciting certain flowinstabilities in the exhaust stream. In one form, the energy source isan electric current source capable of delivering high current betweenadjacent electrodes. At least a portion of the electrodes can be groupedsuch that a pair (or more) within the group defines an actuator. In apreferred embodiment, the groups of electrodes are formed in pairs. Theaforementioned actuators, which can be placed in many ductconfigurations (including axisymmetric and non-axisymmetric ones) areconfigured to produce the arc filament plasma that produces thelocalized perturbation.

According to yet another aspect of the invention, a propulsion system isdisclosed. The propulsion system includes a gas generator and an exhaustsystem in fluid communication with the gas generator. The exhaust systemincludes an exhaust duct defining an exhaust stream flowpath surface,and an arc generator cooperative with the exhaust duct. When the arcgenerator is activated while exhaust gas is flowing through the duct, anarc filament plasma is formed that produces a localized perturbation inthe exhaust stream. The arc generator includes numerous electrodesdisposed adjacent the exhaust duct. As before, the electrodes are placedsuch that they do not substantially protrude into the exhaust stream.The arrangement of the electrodes permits the localized perturbation togenerate streamwise vorticity in the effected portion of the exhauststream. As previously discussed, an energy source coupled to theelectrodes is configured to impart enough energy to them so that an arcfilament plasma capable of generating the localized perturbation isformed. Optionally, the gas generator is a gas turbine engine comprisinga compressor, a combustor and turbine. In addition, at least a portionof the electrodes can be arranged in groups (such as the aforementionedpairs) such that each group or pair defines an actuator. Two or more ofthe electrodes can be arranged to be electrically coupled to a commonground electrode. It will be appreciated by those skilled in the artthat such a common ground electrode arrangement is equally applicable tothe other aspects of the invention disclosed herein.

According to still another aspect of the invention, a method of reducingnoise emanating form a flowpath is disclosed. The method includesflowing a fluid along the flowpath and generating an arc filament plasmaat one or more locations along the flowpath to produce at least onelocalized perturbation in a portion of the flowpath, the localizedperturbation configured such that upon its production, streamwisevorticity is formed in the portion of the flowpath.

Optionally, the flowpath is defined by a conduit (such as an enclosedduct). To generate an arc filament plasma, the method includes operatingan arc generator such that upon activation of the generator, an arcfilament is formed that produces the localized perturbation in fluidflowing through the flowpath. In a more specific option, the arcgenerator includes a plurality of electrodes disposed adjacent theflowpath in an unobtrusive way. In addition, the arc generator includesan energy source coupled to the electrodes and configured to impartenough energy to them such that the arc filament plasma capable ofgenerating the localized perturbation is formed. The method may furthercomprise arranging the electrodes in the conduit to define asubstantially flush fit with the surface of the conduit adjacent theflowpath, as well as arranging them around a substantial periphery ofthe flowpath. As before, the conduit can be a substantially axisymmetricexhaust duct or a substantially non-axisymmetric exhaust duct. Inaddition, the arc generator can be operated to energize the electrodesaccording to a predetermined sequence, frequency or both in order toexcite flow instabilities in the flowpath. In one example, theelectrodes can be operated to be in phase (simultaneously on or off)with each other, or out of phase with each other. In one form, theenergy source is an electric current source. In addition, the electriccurrent source can operate at alternating current frequencies of up tohundreds of kHz, and voltages of up to tens of thousand volts. Moreover,the arc filament plasmas can be used to generate the localized flowperturbations via very rapid heating. For example, by taking as low as afew microseconds to cause the heating of the adjacent fluid, a highlydesirable localized accompanying pressure jump is formed to effect therequisite flow perturbation that is otherwise not possible with largesurface area, low-temperature, non-equilibrium plasmas. The method ofreducing noise may further include exciting jet instabilities within theflowpath by generating the arc filament plasma with predeterminedforcing frequencies that match the initial shear layer instabilities oras high as frequencies associated with the flow structures in inertialsubrange. For example, the forcing frequency can be from tens ofkilohertz (kHz) to hundreds of kHz in a laboratory environment.

According to another aspect of the invention, a method of mixing fluidwithin a flowpath is disclosed. The method includes flowing fluidthrough a conduit and operating an arc generator to cooperate with theconduit such that upon activation of the generator during the flow ofthe fluid through the conduit, an arc filament plasma is formed thatproduces a localized perturbation in a portion of the fluid stream. Thearc generator includes a plurality of electrodes disposed adjacent theportion of the fluid stream being perturbed. As before, the electrodesdo not substantially protrude into the fluid stream, and are arrangedsuch that the localized perturbation generates at least one ofstreamwise vorticity or excitation of flow instabilities in the portionof the adjacent fluid stream. Also as before, an energy source iscoupled to the electrodes to impart the energy needed to form thelocalized perturbation. Optionally, the arc generator can be operated toenergize the electrodes according to a predetermined sequence in orderto introduce streamwise vorticity and excite flow instabilities in theflowpath.

According to another aspect of the invention, a method of using an arcfilament plasma discharge to control the flow of exhaust gas in apropulsion system is disclosed. The method includes flowing fluidthrough an exhaust duct and operating an arc generator to cooperate withthe exhaust duct such that upon activation of the generator during theflow of the exhaust gas through the exhaust duct, an arc filament plasmais formed that produces a localized perturbation in the exhaust gas. Thearc generator includes a plurality of electrodes disposed adjacent theportion of the exhaust gas such that the electrodes do not substantiallyprotrude therein, the electrodes arranged such that the localizedperturbation can impart substantial streamwise vorticity in the portionof the exhaust gas; and an electric current source coupled to theelectrodes and configured to impart enough energy thereto such that anarc filament plasma capable of generating the localized perturbation isformed. As previously discussed, the exhaust duct can be substantiallyaxisymmetric or substantially non-axisymmetric. In addition, theelectrodes can be arranged in groups such that each group defines anactuator. In a more particular form of this arrangement, two or more ofthese electrodes can be electrically coupled to a common groundelectrode. In another configuration, each actuator may be made up of apair of electrodes.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The following detailed description of the preferred embodiments of thepresent invention can be best understood when read in conjunction withthe following drawings, where like structure is indicated with likereference numerals and in which:

FIG. 1A illustrates a schematic arrangement of a pair of plasmaactuators with a common ground electrode according to an aspect of thepresent invention as placed in a rectangular exhaust nozzle;

FIG. 1B illustrates a perspective view of an electrode array placed in arectangular exhaust nozzle;

FIG. 2A illustrates an axial view of the formation of streamwisevortices produced by the operation of the electrode arrangement of FIG.1A;

FIG. 2B illustrates an axial view of the formation of a spanwisepressure rise produced by the operation of the electrode arrangement ofFIG. 2A;

FIG. 3 illustrates current traces of two actuators from the array ofFIG. 1B operating out of phase from one another;

FIG. 4A illustrates a cross section of a jet deformed by the plasmaactuators configuration of FIG. 1A;

FIG. 4B illustrates a cross section of a jet deformed by a large tabaccording to the prior art;

FIG. 5A illustrates four electrode pairs, two on the top and two on thebottom of an axisymmetric exhaust nozzle extension;

FIG. 5B illustrates a simplified perspective view of the nozzleextension of FIG. 5A;

FIGS. 6A and 6B illustrate how the actuators of the present inventioncan be used to excite jet instabilities in the axisymmetric exhaustnozzle of FIGS. 5A and 5B to organize structures and to increaseentrainment and mixing;

FIGS. 7A and 7B illustrate how the actuators of the present inventioncan be used to excite jet instabilities in the axisymmetric exhaustnozzle of FIGS. 5A and 5B to reduce entrainment, mixing, and noise;

FIG. 8 illustrates spatial correlation of images similar to those ofFIGS. 6A, 6B, 7A and 7B, and how excitation of the instabilities via theactuators is coupled into the flow; and

FIG. 9 illustrates a turbofan engine into which electrodes according tothe present invention are notionally placed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring first to FIGS. 1A and 1B, a schematic of a localized arcfilament flow control system 1 is shown. The system 1 includes a conduit(shown in the form of a rectangular exhaust nozzle extension 10)configured as a fluid flowpath 15, and an arc generator 20. The system 1includes copper or steel pin electrodes 60 shown embedded into theflowpath surface 12 of exhaust nozzle 10. Electrodes 60 aresubstantially flush mounted into surface 12 in order to avoid protrudinginto the flowpath 15. In one embodiment, each electrode 60 is twomillimeters in diameter, connected to arc generator 20 throughappropriate wiring 25. In a preferred form, each pair of electrodes thatare used together to complete a circuit cooperate as an actuator. Theactuator can be placed in numerous locations within the exhaust nozzle10, thus permitting tailoring of the position of the generated arcfilament plasma. Additional equipment making up the arc generator 20include amplifiers 30, transformers 40 and ballast resistors 50. In theembodiment shown, two electrodes 60 share a ground electrode that iselectrically coupled to ground 80 to complete the electric circuit thatpasses through either or both electrodes 60. In a preferred embodiment,the exhaust nozzle 10 is made from a non-conducting refractory material(such as a ceramic or ceramic composite) to best resist the localizedhigh temperature regime produced by the electrodes 60. A cooling system(not shown) can be placed in heat exchange relationship with the exhaustnozzle 10 to keep local surface temperatures below the maximum nozzleoperating temperature. The use of cooling air from a compressor bypassor a fan duct to cool exhaust duct liners and nozzle flaps, as used inconventional gas turbine engine exhaust systems, could be employed. Theelectrodes 60 can be configured as an array of pairs, forming anactuator. Each actuator then can be powered with variable frequency (upto hundreds of kHz) and amplitude. The array could then be tailored tothe needs of specific flow regimes, including those for aircraft exhaustsystems designed to fly with subsonic and supersonic Mach numbers,including both current civil subsonic and future supersonic aircraft, aswell as military aircraft. An additional benefit of the electrodes 60 isthat they are equally applicable whether the fluid environment is hot(such as encountered in the exhaust duct of a typical aircraft) or cold.

Referring with particularity to FIG. 1B, the dimensions of the exhaustnozzle 10 of the experimental setup is described as follows. The exitdimensions are one-half inch high by one and one-half inches across,producing an aspect ratio of three. It will be appreciated by thoseskilled in the art that while the present inventors incorporated anexperimental setup with exhaust nozzle 10 that were configured tooperate at three discreet Mach numbers, specifically Mach 0.9, 1.3 and2, that other Mach numbers, nozzle dimensions, aspect ratios and shapesare within the scope of the present invention. The electrodes 60 areformed in rows, where each of the electrodes are four millimeters apartin the spanwise direction, while adjacent rows are spaced sixmillimeters apart in the streamwise direction. The downstream row ofelectrodes are spaced four millimeters from the trailing edge of theexhaust nozzle 10. Referring with particularity to FIG. 1A, theconfiguration of the remainder of the experimental setup is described asfollows. The electrodes were powered by a Powertron 3 kilowatt,high-voltage (up to 15 kV root mean square (rms)), variable frequency (2to 60 kHz) AC power supply, which included the two individually excitedamplifiers 30 and two-arm step-up transformer 40. The power supplygenerated two high-voltage output signals used to generate a pair ofeither streamwise or spanwise arc filaments in the flowpath of theexhaust nozzle 10. The power supply frequency and the phase shiftbetween the two AC excitation signals could be independently varied.Experiments were conducted in ideally expanded Mach 0.9, 1.3 and 2.0flows with exhaust nozzle 10 exit static pressure of one atmosphere. Twospanwise arc filaments, lined up in the spanwise direction shown, weregenerated at the AC voltage frequency of 10 kHz, in phase with eachother. Since the arc is initiated twice during each period, in bothpositive and negative peak voltages, the forcing frequency at theseconditions in this specific embodiment is 20 kHz. At all experimentalconditions, the arcs were stable and were not blown off by fluid in theflowpath 15 exiting the exhaust nozzle 10. Flow visualization was usedto assess the effects of forcing on the fluid (air) flowing throughexhaust nozzle 10. While these experiments were carried out using therectangular nozzle shown at airflow Mach numbers of 0.9, 1.3 and 2.0under ideally expanded conditions, the electrodes 60 are equallyapplicable to an axisymmetric exhaust structure, as well as to otherflow velocities, as will be shown and discussed later.

Referring next to FIGS. 2A and 2B, the effects of the localizedperturbations on the formation of streamwise vortices and the inducedpressure patterns are shown. When electrodes 60 are energized, the arcfilament plasma 90 formed in the region between the electrodes 60 mimicsthe presence of a physically rigid body placed in the flowpath. Thiscauses a pressure profile P to form upstream of the arc filament plasma90. This profile P promotes the formation of the pair of localizedstreamwise vortices 95. Although not shown for an axisymmetric nozzleconfiguration, it will be appreciated by those skilled in the art thatthe general principles behind pressure profile buildup and consequentstreamwise vorticity formation are similar. The same holds true also forany flow Mach number.

Control of excitation frequency, amplitude and duty cycle of theelectrode pairs 60, as well as phase shift between adjacent electrodepairs 60 using the variable frequency AC power supply is fairlystraightforward. FIG. 3 shows the time-dependent current traces in twoarc filaments generated in a Mach 1.3 jet flow when they are operated atthe AC voltage frequency of 10 kHz and out of phase with one another.Indeed, it can be seen that the current in filament A reaches maximum(about 0.4 A) when the current in filament B approaches zero (i.e. whenthe arc is extinguished). This shows that by varying the phase shiftbetween the two AC excitation signals, periodic Joule heat releasepatterns in multiple filaments can be accurately controlled. It canlikewise be seen that the heat release pattern is indeed periodic at afrequency equal to double the input AC voltage frequency in thisspecific embodiment. Most importantly, the time-averaged power at theseconditions is only about 180 Watts, with a substantial fraction of thatbeing dissipated in a 500 ohm ballast resistor connected in series withthe electrode gap to stabilize the discharge. The time-averaged powergenerated in the discharge gap and actually coupled to the flow is onlyabout 50 W per pair of electrodes 60. Comparing this to a kinetic energyflux of the jet of about 22 kW in this laboratory experiment (based on amass flow rate of 0.3 kilograms per second and flow velocity 380 metersper second) at these conditions reveals that the total plasma powerrequirement per electrode 60 pair is about 0.8% of the flow power, whilethe power coupled to the flow by every electrode 60 pair is only about0.2% of the flow power, thus demonstrating the highly energy efficientnature of the present process. Moreover, this is scalable to high massflow rate flows. Also, unlike non-equilibrium plasmas, smallhigh-temperature arcs are not subjected to various instabilities, whichmake possible their use at pressures exceeding one atmosphere.

FIG. 4A shows an average image of an ideally expanded Mach 1.3rectangular exhaust nozzle with the two plasma actuators of FIG. 1Aturned on at forcing frequency of 20 kHz. The image is an average of 25instantaneous (9 nanosecond exposure time) images obtained using apulsed Neodymium Yttrium Aluminum Garnet (Nd:YAG) laser operating at afrequency of 10 Hz (the total run time of about 2.5 sec). The laserpulses were not phase-locked with the AC voltage and thus the average isobtained from 25 consecutive instantaneous images. A sheet of spanwiselight was passed orthogonal to the exhaust jet centerline along theY-axis at eight jet heights along the X-axis (where the jet height isone half inch) downstream of the exit. The bright region in the imagesis the jet mixing layer, where line 90 is shown to track the generalshape of the flow deformation induced by the energized electrodes. Thebright region in the figure is illuminated via scattering of the laserlight by the order of 50 nanometer water particles in the mixing layer.These particles are generated by condensation of moisture in theentrained ambient air when it mixes with the cold and dry jet air. Theshape of a nearly rectangular mixing layer is deformed due to thepresence of the pair of streamwise vortices (previously shownschematically in FIG. 2A). In addition to the deformation, it can beseen that the scattered light intensity in the lower part of the mixinglayer dramatically increases. This implies significant increase of theentrained ambient air into the mixing layer due to streamwise vorticesgenerated by the electrodes. The plasma actuators turn on and off,thereby generating streamwise vortices and causing intermittentdeformation in the jet cross section. FIG. 4B shows a similar behaviorof an axisymmetric Mach 1.3 jet cross section when a large tab is placedin the jet flowpath. In contrast to the intermittent vortices formed bythe plasma actuators of FIG. 4A, the large tab generates a pair ofstreamwise vortices continuously, causing concomitant continuousdeformation in the jet cross section. The size of the tab is a bigfactor in the strength of the streamwise vortices and jet deformation.

Referring next to FIGS. 5A and 5B, in addition to being used for thegeneration of streamwise vortices, the present electrodes 160 could beused in an axisymmetric exhaust nozzle 110 for excitation of jetinstabilities, where four pairs of electrodes 160 are located aroundportions of the nozzle flowpath. It will be appreciated by those skilledin the art that any jet flow, whether through an axisymmetric orrectangular conduit (or any other shape), has certain inherentinstabilities. By providing disturbances with a frequency associatedwith one of the instabilities in the flow, the disturbances will growand affect the flow. By keeping the distance between two electrodes verysmall, or by lining them up in streamwise direction, the generatedstreamwise vortices can be made very small or virtually eliminated.Turning the electrodes on and off with a preferred frequency will havethe effect of exciting a particular jet instability. In the presentexample, the exit diameter D of the experimental exhaust nozzle 110(also designed for Mach 0.9, 1.3 or 2.0 flow speeds) was set at oneinch. As previously mentioned, the electrodes 160 can be operated eitherin phase or out of phase with respect to one another. Time resolvedpressure measurements with the present configuration revealed an initialjet shear layer instability frequency of about 60 kHz for the baselinejet.

FIGS. 6A and 6B show instantaneous jet streamwise images (approximately9 nanosecond exposure time) of Mach 1.3 ideally expanded jet for thebaseline case of FIG. 6A (where the electrodes are turned off) and forthe operating case of FIG. 6B (where all four electrode pairs areenergized and operating in-phase and forcing the jet at 10 kHz). The ticmarks are one nozzle exit diameter (D) apart, with the first one locatedat ID. As can be seen in FIG. 6A, the baseline case has large scalestructures that are not organized and are distributed randomly in space.Contrarily, in FIG. 6B exciting the jet instabilities with plasmaactuators regulates the structures into spatially quasi-periodicstructures, where the wavelength (spacing) of large scale structures iscommensurate with the 10 kHz forcing frequency. This forcing frequencyis twice the jet column instability frequency, but still within the jetcolumn excitation frequency range. In such an excited state, theentrainment and mixing will increase. As before, only the mixing regionis visualized and the intensity of light in the mixing region isdirectly related to entrainment of the moist ambient air into the jet.

FIGS. 7A and 7B show instantaneous jet streamwise images (approximately9 nanosecond exposure time) of Mach 1.3 ideally expanded jet for thebaseline case of FIG. 7A (where the electrodes are turned off) and forthe operating case of FIG. 7B (where all four electrode pairs areenergized and operating in-phase and forcing the jet at 60 kHz). As withFIGS. 6A and 6B, the tic marks are one nozzle exit diameter (D) apart,with the first one located at 1D. While FIG. 7A is the same as the imagein FIG. 6A, showing the baseline case, FIG. 7B shows an image of thesame jet but with much smaller structures and much less entrainment andmixing, due to the higher excitation frequency that is coupled to theflow. This forcing frequency is close to jet initial shear layerinstability frequency and would find many applications, especially inrelation to jet noise reduction. Since the presence of large scalestructures are responsible for a major portion of jet noise, anyreduction in the dynamics associated with such structures would producea concomitant reduction in jet noise.

If the convective velocity and the spacing (or the wavelength) oflarge-scale structures shown in the images of FIGS. 6A, 6B, 7A and 7Bare determined, one can then obtain approximate shedding frequencies ofthese structures and thus the response of the jet to forcing. Thespacing between the structures can be determined manually from theimages, or could be obtained using spatial-correlation of the images.Referring next to FIG. 8, the average spatial correlation over 50instantaneous streamwise images similar to those in FIGS. 6 and 7 isshown. Spatial correlation is a statistical technique which showsquantitatively how well organized or how random the large scaleturbulence structures in a given flow is. If there is no organization ofstructures, then the peak correlation level of 1 at zero x/D separationin FIG. 8 will continuously drop as the separation is increased. This istypical of the baseline case with actuators off. If structures are wellorganized, then following 1 at zero x/D, the correlation will decreasewith x/D, but will go through local peaks and valleys, as is the casefor example for actuators operating at 9 kHz. The distance between twopeaks or valleys is directly related to the forcing frequency. Theseresults are consistent with the flow visualization results shown inFIGS. 7A and 7B.

The distance between the local maxima in FIG. 8 is equivalent to thespatial wavelength (or the spacing) of the periodic structures. Thiswavelength can be used along with the convective velocity of thestructures to determine the shedding frequency of the structures. Theaverage convective velocity for this jet was measured at 266 meters persecond. The measured average convective velocity was used along with thespatial wavelength determined from FIG. 8 to estimate the sheddingfrequency of the structures in the forced jet. It is clear from theresults that the jet responds to the plasma actuator forcing, whererobust quasi-periodic structures develop with strong spatialcorrelations at lower forcing frequencies, and much smaller and lessrobust structures at higher forcing frequencies. Accordingly, theactuators have wide bandwidth and strong authority to force the jet atany of its instabilities and affect the jet in any desired fashion.

Referring next to FIG. 9, a simplified schematic of a turbofan engineused to power an aircraft is shown. The engine 1000 includes an inlet1100, fan 1200, compressor 1300, combustor 1400, turbine 1500 (typicallyincluding a high pressure turbine 1510 and a low pressure turbine 1520)and exhaust nozzle 1600. Cowling 1700 is used to shroud most of theengine 1000, while the fraction of the air passes through the core (thelatter of which is made up of the aforementioned compressor 1300,combustor 1400, turbine 1500 and exhaust nozzle 1600) with the remainderbypassed through the fan 1200 between the core and the cowling 1700. Theair exiting the exhaust nozzle 1600 generate two mixing regions, wherenoise is generated, one between the core flow and the fan flow andanother between the fan flow and the ambient air. Electrodes 1060according of the present invention would be placed in the ducting thatmakes up the exhaust nozzle 1600. A representative placement of theelectrodes 1060 in the core and fan flow (without the remainder of theflow control system) is shown along the outer wall of the flowpath ofthe core nozzle and the fan nozzle, respectively, of the exhaust nozzle1600. Cooling air for portions of exhaust nozzle 1600 situated adjacentelectrodes 1060 could be provided by bleeding off portions of airproduced by compressor 1300 or bypass air produced by fan 1200.

Having described the invention in detail and by reference to preferredembodiments thereof, it will be apparent that modifications andvariations are possible without departing from the scope of theinvention defined in the appended claims. More specifically, althoughsome aspects of the present invention are identified herein as preferredor particularly advantageous, it is contemplated that the presentinvention is not necessarily limited to these preferred aspects of theinvention.

1. A fluid stream flow modification system comprising: a fluid streamconduit configured to receive flowing fluid from a fluid source; and anarc generator cooperative with said conduit such that upon activation ofsaid arc generator during the flow of said fluid through said conduit,an arc filament is formed that produces a localized perturbation in aportion of said fluid stream, said arc generator comprising: an energysource; and a plurality of electrodes coupled to said energy source,said electrodes disposed adjacent said portion of said fluid stream suchthat said electrodes do not substantially protrude therein, saidelectrodes arranged such that said localized perturbation generatesstreamwise vorticity in said portion of said fluid stream.
 2. The systemof claim 1, wherein said energy source is an electric current source. 3.The system of claim 1, wherein said electrodes are disposed in saidconduit to define a substantially flush fit with the surface of saidconduit adjacent said fluid stream.
 4. The system of claim 1, whereinsaid electrodes are configured in at least one row.
 5. The system ofclaim 4, wherein said electrodes are configured in a plurality of rowssuch that each successive row is axially downstream in said conduitrelative to its immediately preceding row.
 6. The system of claim 1,wherein said electrodes are disposed adjacent a trailing edge of saidconduit.
 7. The system of claim 1, wherein said conduit is a duct. 8.The system of claim 7, wherein said duct is substantially axisymmetric.9. The system of claim 8, wherein said electrodes are disposed aroundthe periphery of said duct.
 10. The system of claim 9, furthercomprising a controller coupled to said arc generator such that thegeneration of said localized perturbations at said electrodes occurs ata predetermined time.
 11. The system of claim 10, wherein saidgeneration of said localized perturbations at said electrodes occursstaggered time intervals.
 12. The system of claim 10, wherein saidgeneration of said localized perturbations at said electrodes occurssimultaneously.
 13. The system of claim 1, wherein said duct issubstantially non-axisymmetric.
 14. The system of claim 13, wherein saidsubstantially non-axisymmetric duct is rectangular.
 15. The system ofclaim 1, wherein said conduit is comprised of a refractory material. 16.The system of claim 15, wherein said refractory material comprises atleast one of a ceramic or a ceramic composite.
 17. The system of claim1, further comprising a coolant supply placed in heat exchangerelationship with said conduit.
 18. The system of claim 1, wherein atleast two of said electrodes cooperate with each other to define anactuator, said actuator configured to produce said arc filament thatproduces said localized perturbation.
 19. An exhaust system comprising:an exhaust duct defining an exhaust stream flowpath surface therein; andan arc generator cooperative with said exhaust duct such that uponactivation of said arc generator during the flow of said exhaust stream,an arc filament plasma is formed that produces a localized perturbationin a portion of said exhaust stream, said arc generator comprising: anenergy source; and a plurality of electrodes coupled to said energysource, said electrodes disposed adjacent said portion of said exhauststream such that said electrodes do not substantially protrude therein,said electrodes arranged such that said localized perturbation generatesstreamwise vorticity in said portion of said exhaust stream.
 20. Theexhaust system of claim 19, wherein said electrodes are disposed in saidexhaust duct to define a substantially flush fit with said exhauststream flowpath surface.
 21. The exhaust system of claim 19, whereinsaid exhaust duct is substantially axisymmetric.
 22. The exhaust systemof claim 19, wherein said exhaust duct is substantiallynon-axisymmetric.
 23. The exhaust system of claim 19, wherein saidelectrodes are arranged around a substantial periphery of said exhauststream flowpath surface.
 24. The exhaust system of claim 23, furthercomprising a controller coupled to said arc generator, said controllerconfigured to energize said electrodes according to a predeterminedsequence in order to excite at least one flow instability in saidexhaust stream.
 25. The exhaust system of claim 19, wherein at least aportion of said electrodes are grouped such that each group defines anactuator, said actuator configured to produce said arc filament plasmathat produces said localized perturbation.
 26. The exhaust system ofclaim 25, wherein said each group comprises a group of two of saidelectrodes.
 27. The exhaust system of claim 19, wherein said energysource is an electric current source.
 28. A propulsion systemcomprising: a gas generator; and an exhaust system in fluidcommunication with said gas generator, said exhaust system comprising:an exhaust duct defining an exhaust stream flowpath surface therein; andan arc generator cooperative with said exhaust duct such that uponactivation of said arc generator during the flow of said exhaust stream,an arc filament plasma is formed that produces a localized perturbationin a portion of said exhaust stream, said arc generator comprising: anenergy source; and a plurality of electrodes coupled to said energysource, said electrodes disposed adjacent said portion of said exhauststream such that said electrodes do not substantially protrude therein,said electrodes arranged such that said localized perturbation generatesstreamwise vorticity in said portion of said exhaust stream.
 29. Thepropulsion system of claim 28, wherein said gas generator is a gasturbine engine comprising: a compressor; a combustor in fluidcommunication with said compressor; and a turbine fluidly disposedbetween said combustor and said exhaust system, said turbinerotationally cooperative with said compressor.
 30. The propulsion systemof claim 28, wherein at least a portion of said electrodes are arrangedin pairs such that each of said pairs defines an actuator thereby. 31.The propulsion system of claim 28, wherein a plurality of saidelectrodes are electrically coupled to a common ground electrode.
 32. Amethod of reducing noise emanating from a flowpath, said methodcomprising: flowing a fluid along said flowpath; and generating an arcfilament plasma at one or more locations along said flowpath to produceat least one localized perturbation in a portion of said flowpath, saidlocalized perturbation configured such that upon its production,streamwise vorticity is formed in said portion of said flowpath.
 33. Themethod of claim 32, wherein said flowpath is defined by a conduittherearound, and said generating an arc filament plasma comprisesoperating an arc generator to cooperate with said conduit such that uponactivation of said arc generator during the flow of said fluid throughsaid conduit, an arc filament plasma is formed that produces saidlocalized perturbation and attendant streamwise vorticity.
 34. Themethod of claim 33, further comprising configuring said arc generator tocomprise: a plurality of electrodes disposed adjacent said portion ofsaid flowpath such that said electrodes do not substantially protrudetherein; and an energy source coupled to said electrodes and configuredto impart enough energy thereto such that an arc filament plasma capableof generating said localized perturbation is formed.
 35. The method ofclaim 34, further comprising arranging said electrodes in said conduitto define a substantially flush fit with the surface of said conduitadjacent said flowpath.
 36. The method of claim 34, wherein at least aportion of said electrodes are arranged in groups such that each of saidgroups defines an actuator thereby.
 37. The method of claim 34, whereinat least one of said groups comprises a pair of electrodes.
 38. Themethod of claim 34, further comprising arranging said electrodes arounda substantial periphery of said flowpath.
 39. The method of claim 33,wherein said conduit comprises a substantially axisymmetric exhaustduct.
 40. The method of claim 33, wherein said conduit comprises asubstantially non-axisymmetric exhaust duct.
 41. The method of claim 33,further comprising operating said arc generator to energize saidelectrodes according to a predetermined sequence in order to excite atleast one flow instability in said flowpath.
 42. The method of claim 34,wherein said energy source is an electric current source.
 43. The methodof claim 42, further comprising operating said electric current sourceat alternating current frequencies of up to hundreds of thousand Hertz.44. The method of claim 42, further comprising operating said electriccurrent source at voltages of up to tens of thousand volts.
 45. Themethod of claim 33, wherein said localized flow perturbations areproduced by heating said flowpath with said arc filament to effectconcomitant pressure increases in said filament.
 46. The method of claim32, wherein said method of reducing noise emanating from a flowpathcomprises producing jet instabilities within said flowpath by generatingsaid arc filament plasma with a predetermined minimum forcing frequency.47. A method of mixing fluid within a flowpath, said method comprising:flowing fluid through a conduit; and operating an arc generator tocooperate with said conduit such that upon activation of said arcgenerator during the flow of said fluid through said conduit, an arcfilament plasma is formed that produces a localized perturbation in aportion of said fluid stream, said arc generator comprising: an energysource; and a plurality of electrodes coupled to said energy source,said electrodes disposed adjacent said portion of said fluid stream suchthat said electrodes do not substantially protrude therein, saidelectrodes arranged such that said localized perturbation generates atleast one of a streamwise vorticity or a flow instability in saidportion of said fluid stream.
 48. The method of claim 47, furthercomprising operating said arc generator to energize said electrodesaccording to a predetermined sequence in order to introduce both astreamwise vorticity and a flow instability in said flowpath.
 49. Amethod of using an arc filament plasma discharge to control the flow ofexhaust gas in a propulsion system, said method comprising: flowingfluid through an exhaust duct; and operating an arc generator tocooperate with said exhaust duct such that upon activation of said arcgenerator during the flow of said exhaust gas through said exhaust duct,an arc filament plasma is formed that produces a localized perturbationin a portion of said exhaust gas, said arc generator comprising: anelectric current source; and a plurality of electrodes coupled to saidelectric current source, said electrodes disposed adjacent said portionof said exhaust gas such that said electrodes do not substantiallyprotrude therein, said electrodes arranged such that said localizedperturbation generates streamwise vorticity in said portion of saidexhaust gas.
 50. The method of claim 49, wherein said exhaust duct issubstantially axisymmetric.
 51. The method of claim 49, wherein saidexhaust duct is substantially non-axisymmetric.
 52. The method of claim49, wherein said electrodes are arranged in groups such that each saidgroup defines an actuator.
 53. The method of claim 52, wherein aplurality of said electrodes are electrically coupled to a common groundelectrode.
 54. The method of claim 49, wherein each said group comprisesa pair of electrodes.